You don't need a degree in accounting, nor do you need a degree in anything for that matter! All you need is a few good A levels showing numerical skills, then you take exams through the ACCA/CIMA/ICAEW. You might do this via a practice, as they fund your training and give you on-the-job experience (provided you don't fail any exams), and then you'll be a fully dledged chartered accountant! Bear in mind, the exams are very tough, but if you don't do a degree, you'll be well ahead of your peers who undertake a degree in accounting; They'll only be exempt from a few exams, but they'll still have to be professionally trained like you. But by all means do the degree if you want the university life, i'm jsut saying that it is not necessary to become a chartered accountant.
hope this helps and good luck!